Related papers: On Admissible States of Quantum Fourier Transform
Discrete Fourier transform (DFT) is the base of modern signal or information processing. 1-Dimensional fast Fourier transform (1D FFT) and 2D FFT have time complexity O(NlogN) and O(N^2logN) respectively. Quantum 1D and 2D DFT algorithms…
We consider a partial trace transformation which maps a multipartite quantum state to collection of local density matrices. We call this collection a mean field state. The necessary and sufficient conditions under which a mean field state…
A conventional quantum phase transition (QPT) can be accessed by varying a real parameter at absolute zero temperature. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the QPT in non-Hermitian…
Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free…
We define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties like the Fourier inversion formula, and give some applications. The definition of the holomorphic Fourier transform…
Quantum-matter theory (QMT), based on the Schr\"odinger or Dirac equations, is firmly established for both intra- and intermolecular interactions. However, there are two key issues with QMT. First, its applicability to large molecular…
The Quantum Fourier Transformation ($QFT$) is a key building block for a whole wealth of quantum algorithms. Despite its proven efficiency, only a few proof-of-principle demonstrations have been reported. Here we utilize $QFT$ to enhance…
We have implemented a Walsh-Hadamard gate, which performs a quantum Fourier transform, in a superconducting qutrit. The qutrit is encoded in the lowest three energy levels of a capacitively shunted flux device, operated at the optimal…
Rapid development in quantum computing leads to the appearance of several quantum applications. Quantum Fourier Transformation (QFT) sits at the heart of many of these applications. Existing work leverages SAT solver or heuristics to…
We rationalize the somewhat surprising efficacy of the Hadamard transform in simplifying the eigenstates of the quantum baker's map, a paradigmatic model of quantum chaos. This allows us to construct closely related, but new, transforms…
In this study, the security of Novel Enhanced Quantum Representation (NEQR) of quantum images are suggested by using the Quantum Fourier Transform (QFT) with blind trent. In the protocol, QFT and keys are used to share signature with…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
The codification in higher dimensional Hilbert Spaces (whose logical basis states are dubbed qudits in analogy with bidimensional qubits) presents various advantages both for Quantum Information applications and for studies on Foundations…
By recourse to tempered ultradistributions, we show here that the effect of a q-Fourier transform (qFT) is to map {\it equivalence classes} of functions into other classes in a one-to-one fashion. This suggests that Tsallis' q-statistics…
A general protocol in Quantum Information and Communication relies in the ability of producing, transmitting and reconstructing, in general, qunits. In this letter we show for the first time the experimental implementation of these three…
Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock…
This is a further explanation of a new and simple renormalization approach recently proposed by the author (hep-th/9708104, Ref. [1], that is somewhat sketchy) for any ordinary QFT (whether renormalizable or not) in any spacetime dimension.…
To visualize a higher dimensional object it is convenient to consider its two-dimensional cross-sections. The set of quantum states for a three level system has eight dimensions. We supplement a recent paper by Goyal et al by considering…